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Efficient out-of-core algorithms for linear relaxation using blocking covers

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3 Author(s)
C. E. Leiserson ; Lab. for Comput. Sci., MIT, Cambridge, MA, USA ; S. Rao ; S. Toledo

When a numerical computation fails to fit in the primary memory of a serial or parallel computer, a so-called “out-of-core” algorithm must be used which moves data between primary and secondary memories. In this paper, we study out-of-core algorithms for sparse linear relaxation problems in which each iteration of the algorithm updates the state of every vertex in a graph with a linear combination of the states of its neighbors. We give a general method that can save substantially on the I/O traffic for many problems. For example, our technique allows a computer with M words of primary memory to perform T=Ω(M1/5) cycles of a multigrid algorithm for a two-dimensional elliptic solver over an n-point domain using only Θ(nT/M1/5) I/O transfers, as compared with the naive algorithm which requires Ω(nT) I/O's

Published in:

Foundations of Computer Science, 1993. Proceedings., 34th Annual Symposium on

Date of Conference:

3-5 Nov 1993